Personally I see the advantages of the Cobra Maneuver, but I'm not a fighter-pilot, so what I say probably doesn't matter.
Anyway, one advantage is that performing the Cobra can throw off your pursuer, forcing him to turn away to avoid slamming into you(Since you are essentially slaming on the breaks), and with some luck, line you up for a cheap cannon-kill . (This also applies to missiles if your plane has rear-lockon ability)
The only two downsides is that are the 'to's. The enemy being 'to' close (they can ram you in this case), and/or you being 'to' close to the ground to recover (faceplant into ground = not fun!).

Personally, I'd drop the tanks prior to entering a close-range dog-fight. shedding that extra wieght might give me some extra help in both speed an maneuverability. Not to mention, if those tanks take a hit from a single API round, the result isn't going to be pretty. granted, this is coming from someone who's never been in a real air-battle (just simulated) and was a groundpounder (infantry), so thats up to the fighter-jocks to decide.